通过IAU最新公布的撞击坑名录、"嫦娥一号"影像与DEM数据,本文使用数理统计和空间分析的方法研究了月球正面撞击坑分布的空间不均衡性。主要体现在:(1)月球正面直径较大的撞击坑主要分布在月陆区域,且集中趋势明显,而月海区域直径较大的撞击坑分布较少,周围有大量直径较小的撞击坑;(2)直径较大的撞击坑在月表具有一定随机性,而直径较小的撞击坑在月表的集中性明显; (3)赤道区域的撞击坑密度小于两极区域,前导半球的撞击坑数量小于后随半球;月海区域的撞击坑密度小于月陆区域;密度最大的区域位于月球正面的中南部;(4)月球正面深度大于2.5km的撞击坑主要集中在月陆区域,且在南极的中央经线附近更为集中;在57°N至24°S之间,深径比处于较高水平,最大值出现在14°N附近,均值在0.14左右波动,自该区域至南北两极,深径比逐渐减小,并在南极附近出现最小值;(5)月陆区域撞击坑坡度最大值的均值大于月海区域;坡度最大值的均值规律性明显,即自赤道至两极,撞击坑坡度最大值的均值逐渐增大。月球撞击坑的空间分布具有一定空间集聚性、经向和纬向差异性,该特征与撞击坑形成理论间的耦合关系仍需深入研究。
The mathematical statistics and spatial analyses for lunar near side impact craters are used to unravel potential spatial heterogeneity based on the crater nomenclature released by International Astronomical Union (IAU) and topography and imagery data from Chang'E-1(CE-1).The spatial heterogeneity is mainly embodied in the following aspects: (1)the craters with larger diameters dominantly distribute in the highland and show obvious concentration tendency, however, the mare have much fewer larger craters, accompanying by munificent smaller craters; (2) larger craters have the characteristics of randomness and the smaller crater are concentrated in local areas; (3) density differences: the regions closer to equator have higher crater frequencies than the regions to the pole; the trailing hemisphere is cratered at a higher rate than the leading hemisphere; the most densely cratered region is located in the south-central part of the lunar nearside; (4) depth-diameter ratios differences: the craters with depth larger than 2.5 km almost are found in the highland, and there is a marked concentration of points around the central meridian where it cuts through the southern continent; between 57°N and 24°S, the ratio is at a high level; the maximum value occurs near 14°N, and the average value fluctuates at 0.14; approaching the poles, the ratios are becoming smaller, and the minimum value occurs at the south pole region; and (5) gradient differences: the average of crater's maximum gradient in highland is far greater than the value of craters in mare; the average of crater's maximum gradient shows apparent pattern: from lunar equator to the poles, the average of crater maximum gradient increases gradually. The spatial pattern of lunar craters shows marked regional differentiation characteristics, and the relationship between the pattern and the crater forming theory remains much work to be done before the ultimate goal can be reached.
[1] 欧阳自远. 月球科学概论[M]. 北京:中国宇航出版社, 2005.
[2] Whitaker E A. Mapping and naming the moon-A history of lunar cartography and nomenclature[M]. Landon: Cambridge University Press, 1999.
[3] 刘二中. 技术发明史(第二版)[M]. 合肥: 中国科学技术大学出版社, 2006.
[4] Wilkins H P. Our Moon[M]. Landon: Frederick Muller Ltd, 1958.
[5] Gilbert G K. The Moon's face-A study of the origin of its features[J]. Philosophical Society of Washington Bulletin, 1893,12:241-292.
[6] Dietz R S. The meteoritic origin of the Moon's surface features[J]. Journal of geology, 1946, 54: 359-375.
[7] Joseph A. The astronomical scrapbook: skywatcher, pioneers and seekers in astronomy[M]. Cambrige, Massachusetts: Sky Publishing Corporation, 1984.
[8] Baldwin R B. The face of the Moon [M]. Chicago: University of Chicago Press, 1949.
[9] Baldwin R B. The Measure of the Moon [M]. Chicago: University of Chicago Press, 1963.
[10] Öpik E J. The lunar surfaces as an impact counter . Monthly notices of the Royal Astronomical Society, 1960,120:404-411.
[11] Shoemaker E M. Interpretation of lunar craters . //Kopal Z(ed.). Physics and Astronomy of the Moon. New York: Academic Press, 1962:283-359.
[12] 王世杰,宣焕灿,郑永春,等. 蟾宫览胜-人类认识的月球世界[M].上海:上海科技教育出版社, 2007.
[13] Wilhelms D E. The geological history of the Moon [M]. Washington: United States Government Printing Office, 1987.
[14] Schultz P H. Moon morphology: Interpretations based on Lunar Orbiter photography[M]. Austin: University of Texas Press, 1976.
[15] Doyle F J. Apollo over the Moon: a view from orbit [M]. Washington: Scientific and Technical Information Office (NASA),1978.
[16] Pike R J. Depth/diameter relations of fresh lunar craters: Revision from spacecraft data[J]. Geophysical research letters,1974,1:291-294.
[17] Spudis P D. The geology of multi-ring impact basins: The Moon and other planets[M]. Landon: Cambridge University Press, 1993.
[18] Li C L, Liu J J, Ren X, et al. The global image of the moon by the Chang'E-1: Data processing and lunar cartography[J]. Science Chima (Earth Sciences), 2012,55(1):83-89.
[19] Sawabe Y., Matsunaga T. and Rokugawa S. Automated detection and classification of lunar craters using multiple approaches [J]. Advances in space research, 2006, 37: 21-27.
[20] Urbach E R and Stepinski T F. Automatic detection of sub-km craters in high resolution planetary images[J]. Planetary and space science,2009,57:880-887.
[21] Beals C S. Impact craters and the relative ages of earth and Moon[J]. Nature, 1970,225:368-369.
[22] Nagumo K and Nakamura A M. Reconsideration of crater size-frequency distribution on the Moon: Effect of projectile population and secondary craters[J]. Advances in space research, 2001, 28(8): 1181-1186.
[23] Michael G G. and Neukum G. Planetary surface dating from crater size-frequency distribution measurements: partial resurfacing events and statistical age uncertainty [J]. Earth and planetary science letters, 2010, 294:223-229.
[24] Kopal Z and Carder R W. Mapping of the Moon: Past and Present[M]. Dordrecht: D. Reidel Publishing Company,1974.
[25] "嫦娥一号全月球影像图集"编辑委员会.嫦娥一号全月球图集[M]. 北京:中国地图出版社, 2010.
[26] Tatsch J H. The Moon: Its past development and present behavior[M]. Sudbury, Massachusetts: Tatsch Associates, 1974.
[27] 马程. 空间聚类研究[J].计算机技术与发展, 2009,19(4):134-137.
[28] Wang F H, Hartmann J, et al. GIS-based spatial analysis of Tai place name in southern China: An exploratory study of methodology[J]. Geographic Information Sciences, 2006, 12 (1): 1-8.
[29] 戴晓燕,过仲阳,李勤奋,等. 空间聚类的研究现状及其应用[J].上海地质,2003,4:41-46.
[30] 朱子明,祁新华. 基于Moran's I的闽南三角洲空间发展研究[J]. 经济地理, 2009,29(12):1977-1980.
[31] 杨振山,蔡建明. 空间统计学进展及其在经济地理研究中的应用[J]. 地理科学进展,2010,29(6):757-768.
[32] 孟斌,张景秋,王劲峰,等. 空间分析方法在房地产市场研究中的应用[J]. 地理研究,2005,24(6):956-964.
[33] Anselin L. Local indicators of spatial association-LISA[J]. Geographical analysis,1995,27(2):93-115.
[34] Melosh H J. Impact cratering: A geologic process [M]. New York: Oxford University Press,1989.
[35] Halliday I. The variation in the frequency of meteorite impact with geographic latitude[J]. Meteoritics, 1966,2(3):271-278.
[36] Gallant J, Gladman B, C ＇ uk M. Current bombardment of the Earth-Moon system: emphasis on cratering asymmetries[J]. Icarus, 2009,202:371-382.
[37] Weissman P R., McFadden L A, Johnson T. Encyclopedia of the solar system[M]. San Diego: Academic Press,1999.
[38] Horedt G P and Neukum G. Cratering rate over the surface of a synchronous satellite[J]. Icarus, 1984, 60: 710-717.
[39] Zahnle K, Dones L and Levison H F. Cratering rates on the Gallilean satellites[J]. Icarus,1998,136:202-222.
[40] Barnouin-Jha O S, Zuber M T, Oberst J, et al. Assessing the relationship between crater depth and diameter on Mercury with topographic measurements by MESSENGER . 40th Lunar and Planetary Science Conference, 2009,1638.pdf
[41] Fielder G. Lunar geology [M]. Landon: Lutterworth Press, 1965.
[42] Mazarico E, Watters W A, Barnouin O S, et al. Depth-diameter ratios of small craters from LOLA multi-beam laser altimeter data . 41st lunar and planetary science conference, 2010,2443.pdf
[43] 汤国安,刘学军,闾国年. 数字高程模型及地学分析的原理与方法[M]. 北京:科学出版社,2005.
[44] Gault D E, Quaide W L and Oberbeck V R. Impact cratering mechanics and structures . //French B M and Short N M (eds.). Shock Metamorphism of Natural Materials. Baltimore: Mono Book Corp, 1968.
